No, AIIMS Bhubaneshwar does not permit its students officially to go to the US for clinical experience during the last 1-year internship. There aren't any separate or paid leaves that enable you to avail of this opportunity. However, if you are adamant about going abroad, you can go during vacations or extend your internship. However, one must bear in mind the fact that most electives are of a minimum duration of 1 month so you should balance both things well.
Most medical colleges in India don't allow their interns to take a paid leave for pursuing a thing like this so you should do more research on this. As for JIPMER, I have no information in that regard.